Prisoners' Other Dilemma

26 Pages Posted: 30 May 2003

See all articles by Matthias Blonski

Matthias Blonski

J.W. Goethe University

Giancarlo Spagnolo

Stockholm School of Economics (SITE); Centre for Economic Policy Research (CEPR); University of Rome 'Tor Vergata'; EIEF

Multiple version iconThere are 2 versions of this paper

Date Written: April 2003


Collusive agreements and relational contracts are commonly modeled as equilibria of dynamic games with the strategic features of the repeated Prisoner's Dilemma. The pay-offs agents obtain when being 'cheated upon' by other agents play no role in these models. We propose a way to take these pay-offs into account, and find that cooperation as equilibrium of the infinitely repeated discounted Prisoner's Dilemma is often implausible: For a significant subset of the pay-off discount factor parameter space, all cooperation equilibria are strictly risk dominated in the sense of Harsanyi and Selten (1988). We derive an easy-to-calculate critical level for the discount factor below which this happens, also function of pay-offs obtained when others defect, and argue it is a better measure for the 'likelihood' of cooperation than the critical level at which cooperation is supportable in equilibrium. Our results apply to other games sharing the strategic structure of the Prisoner's Dilemma (repeated oligopolies, relational-contracting models, etc.). We illustrate our main result for collusion equilibria in the repeated Cournot duopoly.

Keywords: Cooperation, collusion, repeated games, relational contracts, risk dominance, cartel stability, strategic risk

JEL Classification: C72, L13, L14

Suggested Citation

Blonski, Matthias and Spagnolo, Giancarlo, Prisoners' Other Dilemma (April 2003). Available at SSRN:

Matthias Blonski (Contact Author)

J.W. Goethe University ( email )

Economics Department
Frankfurt am Main, 60054

Giancarlo Spagnolo

Stockholm School of Economics (SITE) ( email )

P.O. Box 6501

HOME PAGE: http://

Centre for Economic Policy Research (CEPR)

United Kingdom

University of Rome 'Tor Vergata' ( email )

Faculty of Economics - DEI
Via Columbia 2
Rome, RM 00133

EIEF ( email )

Via Due Macelli, 73
Rome, 00187


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